No-regret Dynamics and Fictitious Play

TL;DR

This paper explores the relationship between potential-based no-regret dynamics and fictitious play, showing how these dynamics converge to Nash equilibria and offering simpler proofs for these results.

Contribution

It establishes a connection between no-regret dynamics and fictitious play, providing alternative, shorter proofs of convergence to Nash equilibria.

Findings

No-regret dynamics relate to epsilon-best reply dynamics.

These dynamics converge to Nash equilibria.

Simplified proofs of convergence are provided.

Abstract

Potential based no-regret dynamics are shown to be related to fictitious play. Roughly, these are epsilon-best reply dynamics where epsilon is the maximal regret, which vanishes with time. This allows for alternative and sometimes much shorter proofs of known results on convergence of no-regret dynamics to the set of Nash equilibria.